Finding the Third Proportional to 2,377 and 5,164

Step by Step Solution

1. Step 1: Write the proportion equation
   2,377 : 5,164 = 5,164 : x
2. Step 2: Convert to fraction form
   2,377/5,164 = 5,164/x
3. Step 3: Cross multiply
   2,377x = 5,164 × 5,164
4. Step 4: Simplify right side
   2,377x = 26,666,896
5. Step 5: Solve for x
   x = 26,666,896/2,377
6. Step 6: Final answer
   x = 11,218.72